Question

A vector A which has magnitude of 6 is added to a vector B which is along x-axis. The resultant of two vectors A and B lies along y-axis and has magnitude twice that of the magnitude of vector B. the magnitude of vector B is

Answer 1

6/√5

Explanation:

let unit vector along x and y axis be i and j

according to question

6 + Bi = 2Bj

6 = 2Bj - Bi

6 = √2B^2 + B^2

= 6 = √5B^2

b = 6/√5

Answer 2

Answer:

$\frac{6}{\sqrt{5} }$

Explanation:

Given:

A vector B that is along the x-axis is added to a vector A that has a magnitude of 6.

To find:

Magnitude

Soution:

An item that has both a magnitude and a direction is called a vector. The two prime examples of vector quantities are force and velocity. Similar to how the speed of any object is related to the velocity, understanding the magnitude of the vector would show the strength of the force.

As we all know, a vector is a mathematical object that has both magnitude and direction. Now, let's say that we need to determine the length of any given vector in addition to its magnitude. The vector quantities include things like velocity, displacement, force, momentum, etc.

From the question,

A+Bi=Rj

here  R is the resultant vector

As given,

R=2B

so,

A+Bi=2Bj

A=2Bj-Bi

$A^{2}=4B^{2} +B^{2} =5B^{2}$

A=6

$36=5B^{2} \\B=\sqrt{\frac{36}{5} } \\=\frac{6}{\sqrt{5} }$

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